SWBAT demonstrate understanding of the unit circle and graphing trigonometric functions.

Start class with a matching activity and then assess students with a quiz.

20 minutes

For the first activity today, each student will be given one card from the Ferris Wheel Match cards. Each of the 15 rows of cards are a pair. Each pair will have one equation and either one diagram of a Ferris wheel or a description of a Ferris wheel.

**Note**: for all of the Ferris wheels, we will assume that the rider will always board at the lowest point.

Students will each get a card and will have to walk around the room to find their match. Keep a copy of the cards before they are cut out so you can quickly check that students found their correct pair.

After students find their correct match, they are to look at their Ferris Wheel diagram or description and change one of the numbers. Then, they are to write a new equation that will describe the new Ferris wheel after the number has changed. I talk more about this in the video below.

Once all (or most) of students have completed a revised equation, discuss how each of the measurements affect the equation.

- Ask a group that changed the radius or the diameter of the Ferris wheel to describe how it affected their equation. Ask the students to be specific about which transformation had to change (the vertical stretch in this case).
- Do the same for the length of one rotation.
- Do the same with the height of the Ferris wheel off of the ground.

Summarize how each measurement transforms the equation.

25 minutes

After the matching activity, students will take a short quiz over the unit circle and the graphs of trigonometric functions. The questions included in the document below are sample questions for the quiz. I am not allowing calculators for this quiz because I want it to be an assessment of whether they understand these concepts. For example, for Question #1 a student could get the correct answer using a graphing calculator with very little understanding of how a cosine function behaves and how the transformations affect the graph.